 My paper is also a heuristic. It is about spatial uncertainty and I would like you to think as I give you my paper about a fundamental question which I'm trying to get at but which I haven't solved. And that's a question is a question like Paul's is what is the nature of prehistoric space and what is the nature of modern space and how people conceive of it? And my paper the real question I want to ask is does spatial uncertainty increase or decrease over time? Okay when we go to a new city like Bern and you know this is where Einstein put together time and space. I mean at the Einstein house actually. You know for many of us who've never been here before we get lost very easily but we pull out our telephones or our maps and we usually the GIS systems and we find our way around. Well we're uncertain and is that degree of uncertainty any more or less than the degree of uncertainty that somebody prehistoric who knew their territory but only to a certain extent had. And so that's the fundamental first question I'm kind of interested in. The second question I am interested in is how archaeologists deal with their own spatial uncertainty and my paper is a bit confusing because it combines the two. Okay so spatial uncertainty as Robert Frost you all many of you may remember the poet two roads diverged in a yellow wood he says I don't know what I'm going to do but then he decides I will he's I'm uncertain I'll take the one less taken and that has made all the difference that's a you know kind of and it is a degree of uncertainty of the way people behave. So spatial uncertainty a prehistoric component and then an archaeological component. And why is this an issue? Well it's a basic issue because of all the things that Paul said and because we're actually trying to look for some kind of truth in terms of archaeological disciplines. We're trying to understand the past we're trying to create heritage where we we also have all kinds of modern issues about space and the past with regards to litigation and you know jurisdiction and all that kind of thing right? What is uncertainty? Well uncertainty is a imperfect and inexact knowledge of the world and then we use with regards to our data because we are not exactly sure of what we observe or measure in either society or in nature and Paul gave us some really nice examples of that if you think about you know or uncertainty what's behind us. You know we already have so far distance we can proceed right? And so when we do the deal with that we are and we recognize our uncertainty then we have to be unsure of the conclusions which we reach out of those spatial analyses. So both prehistoric societies and archaeologists both cope with large amounts of spatial and also temporal uncertainty and then I define it for the purposes as being the difference between the phenomena as cultural representation as well as the lack and error in position. So what are some of the sources of spatial uncertainty both prehistorically and for modern reasons? One we have errors in geographic location right? We think we're someplace we're someplace else we think that place is somewhere it's slightly somewhere off. We have partial and incomplete knowledge we only know where half of the city is. We have inappropriate assumptions regarding the environment for example driving in the burn I was supposed to go to the casino plots and I got to the I almost got to the casino plots I couldn't get there incomplete knowledge of the environment the police were blocking all the roads to the casino plots because Netayano was in town on Saturday right? So I'm driving around and around it out of the town in the town. Problems and classification when we talk about a town or we talk about something else is it the same thing lack of pattern recognition and actually even the probability that something exists the probability that it has a location and we can classify spatial uncertainty and this is a whole system for doing so I'm not going to cover it and just let you know it exists and when I write this paper up in more detail there will be a big discussion of it. Let's take a quick look at one example of my own work on spatial uncertainty at the level of the archaeologists okay this is probably relevant for many departments of antiquities in many countries I know it's true for the United States I there was something called the New York State Archaeological Survey it has something like not 85,000 historic and archaeological sites they've been carefully keeping track of these sites for 40 50 50 years at least you know it's at any other department of antiquities so I decided I'd go back and see if I could find the sites that they actually had right 50% were not where they were located right there were errors in location recording there were errors that people said the sites were there but they were destroyed there was errors in classification they said it was a hunting and gathering site it turned out to be you know something in agricultural sites up night well one of the reasons is there was no quality control for negative findings right so nobody went out if somebody said there's no sites there nobody went out and rechecked for example and today of course GPS would probably fix many of the problems but you know something nobody's going back and we check there's errors in geographic location they may be caused by psychological factors so inconsistencies in spatial perception errors may be caused because of mapping both now and prehistorically so what do you do with boundaries for example that's what this little diagram shows about and errors in location may be caused by how spatial information is communicated classified stored and transmitted over time and space prehistorically by word of mouth you're going to go hunting go down to four trees down turn left at the stream go over the stream you know a given distance well maybe it wasn't it's changed by natural language is it what we mean the same thing when we say tree physical representations do we build little models of this well and we have little models of prehistoric maps actually a guy named Patrick Dale and I wrote a paper on prehistoric maps and hunting and gathering maps and how different they were from Mars and markers and how things are classified and you know we just think about it here are some of today's ways of looking at marking space and you can see uncertainly trail markers right boundary markers fences aerial photographs GPS satellite systems all locating space and as I say you know Einstein lived here and you know that as he was in touch with Heisenberg and Heisenberg's famous uncertainty principle right you are probably here but you might actually be there right I mean and that's funny but it's actually a true kind of statement right and it can be applied to prehistoric historic and modern issues and let me give you a wonderful historical example I love the way Paul puts up books and his references so I'm going to do not nearly as good a job I used to one of the things I did was I studied there was a wonderful organization called the Hacker organization that publishes all the captain's logs of all the ships of exploration right and I like to go studying them clever it's interested in where disease got into the new world I'd like trace the ships and see how they the diseases happen and recently going back over some of that stuff I found the following documents about ships log that in 1708 both our good bounty appeared in a periodical called memoirs for the curious and in 1744 this story was revived and in 1752 he published a memoir of this and what it said was in 1640 a Spanish admiral sailed 5000 miles north from Lima the 53 degrees north where he entered the real delos race and did all this wonderful stuff right this is the actual title of his map there's a full reference and this is what it is the map of the great probability of the northwest passage in 1755 they thought about what is the probability I mean what is the probability it's a spatial uncertainty it's truly spatial uncertainty and there you see what they're doing a modern example the path of the hurricane durian as stated on September 1st September 3rd and 6th right on the first it was going all the way up Florida on the third it's supposed to be along the edge of Florida and not and on the 6th it's missing it all together and going up he at these different times spatial uncertainty about a major event so spatial variability occurs everywhere as Paul said it's a universal we are spatially dependent upon therefore I believe an estimate of uncertainty is important it can be descriptive it can be quantitative it can be sensitively it can be based on confidence and it may come really from four different components one because we have non spatially structured environmental variation we have spatially structured environmental variation which is interacting with it and the spatial variation of the variable that we're thinking about may not be shared by the variables and then we have unexplained things that people do that don't actually have spatial variation so how do we handle it well we try to handle it through measurement and we try to determine the amount of sampling error and sometimes we can do it and sometimes we can't and we make mistakes and whether we are prehistoric or modern it may be based upon the equipment we use it may be because of bad data in our collection methods it may be cause of the bad observers and it may be because we mismatch the data collected by different people and or another set of different people just trying to put the sets of information together another very important thing particularly prehistoric way but even today is the semantic uncertainty of space and our spatial terms there's a geographer named David Mark who has spent a lot of time worrying about landscape terms what does it mean when I say creek scream river lake hill Mesa mountain you would think that in a language it is common I speak English pretty much like a native Paul speaks French as pretty much like a native I would make a bet in fact I try this experiment that if I asked Paul and Paul asked me what that thing out there is with the kind of trees out there and I will say I will say to me it looks like a foot hill what would you say it would be in French what we'll find is it doesn't correspond and so what Mark did very interesting self-experience he had pictures and he had people in the same language say give it the name same names all kinds of different words then he did cross language and we discovered it made it even worse and then what you do is you try this little experiment which he and I did as a paper take the word hell in English translated in the German translated using the English German dictionary go from German to French French to Russian Russian back to English and see if you come out with the same word you don't right and what that's just demonstrating to you is that this huge semantic uncertainty in the word Renfrew did the same thing about a sight and future Zubro and Hunt did the same thing about shapes itself what is circular right is this more circular than this with a little notch out of it or something it's circular with a square turns out all kinds of different people have totally different conceptions of the shape of what is circular and other things about okay I'm probably how I do on time we have about off it now okay because so you see that ten minutes okay so one another issue when we compare disparate data sets as archaeologists each of which may have a very different uncertainty structure associated with it such as location depth type of feature how do we actually combine this uncertainty how do we do it cartographically like bands fuzziness of boundaries semi-transparent the kinds of things and if you look at some of the standard solutions that geographers have tried to use they don't work for example spatial order especially of archaeological prettier spatial order other correlation causes false gradients in the data data spatial correlation may show you spurious we because of intervening cultural variables missing areas cause huge spatial uncertainty both now and prehistorically how do we do handle missing areas today we do it intuitively or we do it non-intuitively by extrapolation and interpolation right we extrapolate what we know about this location of burn to another location of burn and we say well if the blocks go this way they're going to keep on going that way and sometimes it works and sometimes it doesn't usually do a random choice here the gentleman with the beard do you think extrapolation works better or interpolation would work better extrapolation is going from a series of points to next point or you have a series of point on one end and those series of points on the other end and you're going to go guess what's in the middle I guess I'm using both strategies like the which one do you think gives you better results well I used one on the Swedish walk about right and so I started asking people about direction and nobody knew the direction because they live and went to the subway and so I went to restart it to ask people with dogs because they walk right and so then I asked people with big dogs in the end because they walk further exactly this is this is perfectly this is exactly the point of a continue well without I guess that shows a kind of having an idea of what where I was just about with regard to the target and I was at the moment with the interpolating aspect and then on the other hand you know I would choose a strategy to whom I would talk to which would be extrapolated exactly and both work generally we have discovered that interpolation works a little bit better than extrapolation but it is but both of them also has the problem of creating spatial uncertainty and we try and these are methods to get towards it okay so even if all the dated values are known without error the combination of the variables may be uncertain so the true form is unknown so back to my original question and I have to say my data I'm still analyzing but I have here the basically fundamental question that I would add to Paul's paper this is a little short part is popular if you look at time the long history of time is we know the following right the number of people are increasing very rapidly and have increased over time we know the amount of spatial information has increased over time right because we know that all those people are adding up more and more spatial information but is the amount of spatial information for a person and the amount of uncertainty increasing over time so we can imagine two different situations in which you could argue and I'll just kind of do the extremes that people free historically if he was going out free historically and asking where a particular location was people would have walked to that location they probably would have known where they were and therefore we will probably say the prehistoric way the degree of uncertainty was probably less than it is for you today on the other hand we might argue and this is what I'm trying to work out with my data at the moment for Paul is maybe it's the other way around that with all these other wonderful pieces of equipment that we have created fences and mats and telephone GPS systems that we actually are better at knowing where we are and where we're going than we were free historically the answer to that question I don't know right it could be either this or could be that but that's what I'm trying to get towards in this paper and my I'm working on the data now from various prehistoric sites and various prehistoric roads to see if I can come up with some kind of proxy to do that so how do we manage this uncertainty and people have come up with various ideas but my suggestion is simply accept it and notice that it is to a greater or lesser extent there's a lot of literature this is the gateway to some of it and then I'll end with where I began if I can with your help and I thought this would be pleasant for you all been here for a long time a self-conference so if we could just do this this is some spatial uncertainty I hope I can you hear it everybody two roads diverged in a yellow wood and sorry I could not travel both and be one traveler long I stood and look down one as far as I could to where it bent in the undergrowth then took the other as justice fair and having perhaps the better claim because it was grassy wanted where though as for that passing there had really worn them about the same and both that morning equally lay and leaves no step and trodden black oh I kept the first for another day yet knowing how way leads on to way I doubted if I should ever come back I shall be telling this with a sigh somewhere ages and ages hence two roads diverged in a wood and I I took the one less traveled by and that has made all the difference